(x-2)(x-2+x+4)=(4)(9)

Average speed = 2.5 miles

Divide 6 from both sides.

6/6 = 1

15/6 = 2.5

So, overall Mark walks 2.5 miles per hour.

hope it helps!

Answer:

Look at the attachment

Answer:

y + 21 = - 4(x - 7)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, - 21) and (x₂, y₂ ) = (- 4, 23)

m = [tex]\frac{23+21}{-4-7}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4

Using m = - 4 and (a, b) = (7, - 21), then

y - (- 21) = - 4(x - 7), that is

y + 21 = - 4(x - 7)

Answer:

Area: T = 0.649

Step-by-step explanation:

Sides: a = 3.5   b = 1.333   c = 2.25

Answer: 480 in^3

Step-by-step explanation:

v= l * w*h

v = 12 * 8 * 5

v=  480

Answer:

$6.75

Step-by-step explanation:

$31.25 = C + 4B C for box of candy and B for large bags of popcorn

$46.50 = 3C + 5B

3($31.25 = C + 4B)

$93.75 = 3C + 12B

-46.50. -3C. -5B

$47.25 = 7B

÷7. ÷7

$6.75. = B

Answer:

A timeframe of 8 years is when there were 45 raccoons in the area.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Equality Properties

Standard Form:
[tex]\displaystyle ax^2 + bx + c = 0[/tex]

Quadratic Formula:
[tex]\displaystyle x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \begin{aligned}y & = 0.4x^2 + 2x + 2 \\y & = 45 \ \text{raccoons} \\\end{aligned}[/tex]

Step 2: Find Specific Year

We are trying to find the year when there were 45 raccoons present in the area. From first glance, we see we probably can't factor the quadratic expression, so let's set up to use the Quadratic Formula:

Now that we have our variables from Standard Form, we can use the Quadratic Formula to find which years when there were 45 raccoons present in the area:

Since time cannot be negative, we can isolate the other root to obtain our final answer:

[tex]\displaystyle\begin{aligned}x & = 8.16536 \ \text{years} \\& \approx \boxed{ 8 \ \text{years} } \\\end{aligned}[/tex]

∴ we have found the approximate amount of years to be 8 years when there were 45 raccoons in the area.

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Learn more about Algebra I: https://brainly.com/question/16442214

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Topic: Algebra I

Answer:

Payton, our equation looks like y = mx + b with m being the slope and b being the y-intercept. We are given a slope of 3, and if the graph passes through the origin, the y-intercept is 0.

Step-by-step explanation:

Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line.

Answer:

The (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.

Step-by-step explanation:

We can solve this question using the concept of z-score or standardized value, which is given by the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

[tex] \\ z[/tex] is the z-score.

[tex] \\ x[/tex] is the raw score.

[tex] \\ \mu[/tex] is the population's mean.

[tex] \\ \sigma[/tex] is the population standard deviation.

Analyzing the question, we have the following data to solve this question:

Therefore, using all this information, we can determine the (population) standard deviation using formula [1].

Then, substituting each value in this formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

Solving it for [tex] \\ \sigma[/tex]

Multiplying each side of the formula by [tex] \\ \sigma[/tex]

[tex] \\ \sigma*z = (x - \mu) * \frac{\sigma}{\sigma}[/tex]

[tex] \\ \sigma*z = (x - \mu) * 1[/tex]

[tex] \\ \sigma*z = x - \mu[/tex]

Multiplying each side of the formula by [tex] \\ \frac{1}{z}[/tex]

[tex] \\ \frac{1}{z}*\sigma*z = \frac{1}{z}*(x - \mu)[/tex]

[tex] \\ \frac{z}{z}*\sigma = \frac{x - \mu}{z}[/tex]

[tex] \\ 1*\sigma = \frac{x - \mu}{z}[/tex]

[tex] \\ \sigma = \frac{x - \mu}{z}[/tex]

Then, this formula, solved for [tex] \\ \sigma[/tex], will permit us to find the value for the population standard deviation asked in the question.

[tex] \\ \sigma = \frac{431.8 - 450}{-0.7}[/tex]

[tex] \\ \sigma = \frac{-18.2}{-0.7}[/tex]

[tex] \\ \sigma = 26[/tex]

Thus, the (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.

Answer: 47,520

Step-by-step explanation: 36 times 40 times 33

Answer:

where's the data

Step-by-step explanation:

Answer:

-3 is greater than or equal to s

Step-by-step explanation:

subtract 3 on both sides

then get s by itself by dividing by -4 on both sides (bc you are dividing by a negative the sign flips)

Answer:

The answer is -18

Step-by-step explanation:

Actually if the x2 is supposed to be x^2 then it's -10

Answer: -18

Step-by-step explanation:

Answer:

(x - 4)² + (y - 5)² = 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (4, 5) and r = 2, thus

(x - 4)² + (y - 5)² = 2², that is

(x - 4)² + (y - 5)² = 4 ← second option on list

The required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2  + (y-5)^2 = 4

The standard equation of a circle is expressed as:

(x-a)^2  + (y-b)^2 = r^2

where:

(a, b) is the centre = (4, 5)

r is the radius = 3 units

Substitute to have;

(x-4)^2  + (y-5)^2 = 2^2

(x-4)^2  + (y-5)^2 = 4

Hence the required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2  + (y-5)^2 = 4

Learn more on equation of circle here: https://brainly.com/question/14150470

Answer:

A and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the quadratic inequality x² - 8x + 15 <0, to get the solution set for the inequality, the following steps must be followed;

Step 1: Factorize the quadratic expression

x² - 8x + 15 <0

x² - 3x - 5x + 15 <0

x(x - 3) - 5(x - 3)  <0

(x -3)(x -5)< 0

x -3<0 and x -5<0

x< 3 and x< 5

Therefore, the solution set for the quadratic inequality are x<3 and x<5

Answer:

(3, 5)

Step-by-step explanation:

Correct on e2020

Answer:

1. the blue one 2. because the blue one have more length.

good luck.

Answer:

1. Blue

2. blue, because i measured both lines with a ruler

3. This one is harder to decide because the blue line was barely longer than the red line

Step-by-step explanation:

I measured the lines with a ruler for this one too.

Answer:

[tex] P(24< X<38)= P(X<38) -P(X<24)= F(38) -F(24)[/tex]

And replacing we got:

[tex] P(24< X<38)=\frac{38-20}{40-20}-\frac{24-20}{40-20}= 0.9-0.2= 0.7[/tex]

Step-by-step explanation:

We can define the random variable X as the thickness of a protective coating applied to a conductor designed to work in corrosive conditions. And the distribution for X is given by:

[tex] X \sim Unif (a = 20, b=40)[/tex]

And we want to find this probability:

[tex] P(24< X<38) [/tex]

And in order to find this probability we can use the cumulative distribution function given by:

[tex] F(x) = \frac{x-a}{b-a} , a\leq X \leq b[/tex]

And if we use this formula for the probability desired we have:

[tex] P(24< X<38)= P(X<38) -P(X<24)= F(38) -F(24)[/tex]

And replacing we got:

[tex] P(24< X<38)=\frac{38-20}{40-20}-\frac{24-20}{40-20}= 0.9-0.2= 0.7[/tex]

Answer:

6.1

Step-by-step explanation:

we will name the length in front of the angle , y :

tan(71°)≅2.904= y ÷2

⇒ y=  5.8

and we know that

c = [tex]\sqrt{2^{2} + y^{2} }[/tex]

then  

c = 6.14

and if we round it to the nearest tenth :

c = 6.1

Answer:

the answer is B

Step-by-step explanation:

hope it help

Answer:

72 degrees

Step-by-step explanation:

A pentagon has five lines of symmetry. For rotation symmetry, the order of any regular polygon is the number of sides. The angle of rotation would be 360 degrees divided by that order. Therefore, the answer is 72 degrees.

Answer:

(1,-2) edge2020

Step-by-step explanation:

Answer:

(1,-2)

Step-by-step explanation:

got it right on edge

Answer:

-3/4

Step-by-step explanation:

Point A is at (-4,3) and Point B is at (4,-3)

The slope is at

m = (y2-y1)/(x2-x1)

   = (-3 -3)/(4 - -4)

   = (-3-3)/(4+4)

    = -6/8

     = -3/4

Answer:

Triple

Step-by-step explanation:

V = π * r^2 *h

h is directly proportional to V so when h increases V increases.

This is a linear relationship so if h is tripled the volume will be tripled as well.

if r tripled then V would be 9 times as large since r has a square relationship with V.

If you're unsure about these just plug in number r= 2, h= 4, and perform the operation they ask you to do (triple or double) and you'll always get it right.

Answer:

X=6 y=3 point form (6,3)

Step-by-step explanation:

Answer:

6,3

Step-by-step explanation:

I just took the test and got 100%

Answer:

taco

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

102-(29 x 3)

Answer:

p=15

Step-byexplanation:

3t+p/102

3(29)+p=102

87+p=102

p=15

Answer:

381623 ft

Step-by-step explanation:

Since the airport altitude is 20000 ft and the pilot needs a 2° descent, to calculate the distance of the airplane at the start of this approach, first this is represented in the diagram attached. The distance from the runway at the start is x.

[tex]tan(3) = \frac{20000}{x} \\x=\frac{20000}{tan(3)} \\x=381623ft[/tex]

The airplane is at a distance of 381623 ft away from the airplane runaway at the start of the descent.

This question is incomplete and it lacks the attached diagram of the square based pyramid. Find attached to this answer, the square based pyramid.

Correct Question

A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.

A. What is the slant height of the pyramid?

B. What is the surface area of the composite figure?

HINT: The surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.

C. How many cubic yards of concrete are needed to make the planter?

Answer:

A. The slant height of the pyramid = 2.24 yards.

B. The surface area of the composite figure = 12.94 square yards.

C. The cubic yards of concrete are needed to make the planter = 2.67 cubic yards.

Step-by-step explanation:

A. What is the slant height of the pyramid?

To calculate the Slant height of a pyramid we make use of the Pythagoras Theorem which is given as:

a² + b² = c²

Where a = Height of the square pyramid represent by h

b = radius of the square pyramid represented by r

c = Slant height of the square pyramid represented by s

Therefore, we have

h² + r² = s²

Looking at the attached diagram, we are given the side length = 2 yards.

The radius of the square based pyramid = side length ÷ 2

= 2÷ 2 = 1 yard.

The height of a square based pyramid = 2 yards

Since , h² + r² = s²

The slant height of the square pyramid is calculated as :

√h² + r² = s

√(2² + 1²) = s

√5 = s

s = 2.24 yards

B. What is the surface area of the composite figure?

We were given hints in the question that the the surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.

Step 1

We find the Lateral area of the faces of the insides of the inverted pyramid

We have 4 faces, Hence,

The formula is given as

a × √( a² + 4h²

a = 2 yards

h = 2 yards

So, = 2 × √( 2² + 4 ×2²

The Lateral area of the faces = 8.94 square yards.

Step 2

Area of the 5 faces of the cube

= a²

Where a = side length = 2 yards

= 2²

= 4 square yards.

Step 3

Therefore, surface area of the composite figure = 8.94 square yards + 4 square yards

= 12.94 square yards.

C. How many cubic yards of concrete are needed to make the planter?

This is calculated by find the Volume of the Square based pyramid.

The formula is given as :

V = (1/3)a²h

Where a = side length = 2 yards

h = height of the square based pyramid = 2 yards

V = 1/3 × 2² × 2

V = 2.67 cubic yards